Articles publicats en revistes (Matemàtiques i Informàtica)

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Pebble trees
(Canadian Mathematical Society., 2025) Pilaud, Vincent
A pebble tree is an ordered tree where each node receives some colored pebbles, in such a way that each unary node receives at least one pebble, and each subtree has either one more or as many leaves as pebbles of each color. We show that the contraction poset on pebble trees is isomorphic to the face poset of a convex polytope called pebble tree polytope. Beside providing intriguing generalizations of the classical permutahedra and associahedra, our motivation is that the faces of the pebble tree polytopes provide realizations as convex polytopes of all assocoipahedra constructed by K. Poirier and T. Tradler only as polytopal complexes.
A Sustainable mHealth Intervention to Promote Physical Activity for Healthy Aging: A Pilot Study of the “Every Walk You Take” Citizen Science Initiative
(MDPI, 2024-06-23) Naik, Preet; Álamo Junquera, María Dolores; Igual Muñoz, Laura; Serrajordi Domènech, Marc; Pérez González, Alba; Pericas Escale, Carles; Pagès Fernández, Constança; Katapally, Tarun Reddy; Grau, Maria
The objective of the Every Walk You Take initiative was to co-design and test, in a pilot study, a sustainable mHealth intervention prototype (mobile app) to promote physical activity. This prototype would help to identify the barriers to and facilitators of active living in individuals older than 55 years. A prototype of the intervention was co-designed by a community of stakeholders in Barcelona who were familiar with the social and economic burden of aging in high-income societies. The app’s functionalities included recommendations for healthy routes in the city (parks, pedestrian lanes, and streets) according to environmental variables (air quality and climate) and personal preferences (route difficulty, distance, and geolocation), and ecological momentary assessments (pictures and voice notes) were collected to identify the barriers to and facilitators of performing these routes. To test the app, a pilot study was conducted over two 7-day cycles with citizen scientists recruited at the life-long learning centers of two deprived neighborhoods in Barcelona. A total of 21 citizen scientists (mean age = 67 (standard deviation = 7)), 86% of them female, collected 112 comments and 48 pictures describing their perceived barriers to and facilitators of active living. Every Walk You Take is a new, validated, and sustainable mHealth intervention that is directly involved in health promotion, as it empowers the citizens of Barcelona to play an active role in their own healthcare. This intervention has the potential to be implemented in different cities around the world to collect information on the community determinants of health and health assets.
Physically Informed 3D Food Reconstruction: Methods and Results
(Institute of Electrical and Electronics Engineers (IEEE), 2026-03-12) Wang, Pengyu; Xi, Pengcheng; Wong, Alexander; Zhu, Fengqing; He, Jiangpeng; Chen, Yuhao; Vinod, Gautham; Zhang, Xiaoyan; Mahmud, Talha Ibn; AlMughrabi, Ahmad; Haroon, Umair; Rodrigues Sepúlveda Marques, Ricardo Jorge; Radeva, Petia; Jueluo, Yawei; Shi, Chengyu
Accurate food portion size estimation is a critical challenge in nutrition analysis and dietary assessment. Recent 3D reconstruction methods primarily focus on surface geometry, often neglecting the volumetric accuracy necessary for precise portion size estimation. In this work, we present three methods, NS-DRS, HR-CMS, and GS-GP, for real-scale 3D food reconstruction and volume estimation from limited 2D inputs. All three methods follow a shared three-stage pipeline consisting of 3D reconstruction, scale estimation using physical references such as visible checkerboards, and mesh refinement. While this high-level structure is consistent, the methods differ in their reconstruction backbones and scale-recovery mechanisms, and are designed for different input conditions, including both single-view and multi-view images. We evaluate each method on a diverse set of food items exhibiting variations in texture, shape, and camera pose, and assess their performance in terms of volume estimation and geometric accuracy. The results reveal complementary strengths among the pipelines, with NS-DRS performing better in volume estimation and GS-GP being more effective in 3D reconstruction. Across all settings, the three methods achieve 18–23% lower volume estimation error compared to the current state-of-the-art model. These findings demonstrate the effectiveness of physically informed and explainable reconstruction pipelines for accurate portion estimation, and support their potential use as scalable tools for dietary monitoring and clinical nutrition analysis.
FoodMem: Near real-time and precise food video segmentation
(Elsevier B.V., 2025-06-01) AlMughrabi, Ahmad; Galán, Adrián; Rodrigues Sepúlveda Marques, Ricardo Jorge; Radeva, Petia
Food segmentation, including in videos, is vital for addressing real-world health, agriculture, and food biotechnology issues. Current limitations lead to inaccurate nutritional analysis, inefficient crop management, and suboptimal food processing, impacting food security and public health. Improving segmentation techniques can enhance dietary assessments, agricultural productivity, and the food production process. This study introduces the development of a robust framework for high-quality, near-real-time segmentation and tracking of food items in videos, using minimal hardware resources. We present FoodMem, a novel framework designed to segment food items from video sequences of 360-degree unbounded scenes. FoodMem can consistently generate masks of food portions in a video sequence, overcoming the limitations of existing semantic segmentation models, such as flickering and prohibitive inference speeds in video processing contexts. To address these issues, FoodMem leverages a two-phase solution: a transformer segmentation phase to create initial segmentation masks and a memory-based tracking phase to monitor food masks in complex scenes. Our framework outperforms current state-of-the-art food segmentation models, yielding superior performance across various conditions, such as camera angles, lighting, reflections, scene complexity, and food diversity.2This results in reduced segmentation noise, elimination of artifacts, and completion of missing segments. We also introduce a new annotated food dataset encompassing challenging scenarios absent in previous benchmarks. Extensive experiments conducted on MetaFood3D, Nutrition5k, and Vegetables & Fruits datasets demonstrate that FoodMem enhances the state-of-the-art by 2.5% mean average precision in food video segmentation and is 58× faster on average. The source code is available at: https://amughrabi.github.io/foodmem
Precision at scale: Domain-specific datasets on-demand
(Elsevier Ltd., 2026-03-01) Molina Rodríguez de Vera, Jesús; González Estepa, Imanol; Sarasúa, Ignacio; Nagarajan, Bhalaji; Radeva, Petia
Recent self-supervised learning methods rely on massive general-domain datasets for robust model pretraining. However, these datasets may lack specificity required in specialized domains. Collecting large, supervised datasets to compensate for this limitation is also cumbersome. This raises a key question: Can automatically crafted domain-specific datasets serve as efficient and effective SSL pretrainers, performing comparable to—or even surpassing—much larger state-of-the-art general-domain datasets? To address this challenge, we propose Precision at Scale (PaS), a novel modular pipeline for automatic creation of domain-specific datasets on-demand. PaS leverages Large Language Models (LLMs) and Vision-Language Models (VLMs) through three distinct phases: Concept Generation, where LLMs identify relevant domain concepts; Image Collection, utilizing VLMs and Generative models to gather appropriate images; Data Curation, ensuring quality and relevance by eliminating unrelated or redundant images. We conduct extensive experiments across three complex domains — food, insects, and birds — proving that PaS datasets compete and often surpass existing domain-specific datasets in diversity, scale, and effectiveness as pretrainers. Models pretrained on PaS datasets outperform those trained on large-scale general-domain datasets (ImageNet-1K) by up to 21 % and surpass same-scale domain-specific datasets by 6.7 % across classification tasks. Notably, despite being an order of magnitude smaller, PaS datasets outperform ImageNet-21K pretraining, with improvements of 3.3 % in fine-tuning and 9.5 % in few-shot learning, and showing superior performance on specialized dense tasks. Furthermore, by efficiently fine-tuning pretrained VLMs like CLIP and SigLIP using low-rank methods, we achieve performance gains (+4.2 % over CLIP) in specialized domains with minimal overhead, demonstrating the versatility of PaS datasets.
Interval hypergraphic lattices
(Elsevier Ltd., 2026-02-01) Bergeron, Nantel; Pilaud, Vincent
For a hypergraph ℍ on [ ] , the hypergraphic poset ℍ is the transitive closure of the oriented skeleton of the hypergraphic polytope △ℍ (the Minkowski sum of the standard simplices △ for all ∈ℍ ). Hypergraphic posets include the weak order for the permutahedron (when ℍ is the complete graph on [ ] ) and the Tamari lattice for the associahedron (when ℍ is the set of all intervals of [ ] ), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of [ ] . We characterize the interval hypergraphs for which is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.
Lp estimates for the Laplacian via blow-up
(Elsevier, 2025-10-05) Lewenstein Sanpera, Jan Bruno; Ros, Xavier
In this note we provide a new proof of the 2, Calderón-Zygmund regularity estimates for the Laplacian, i.e., Δ⁢ = and its parabolic counterpart ∂ − Δ⁢ = . Our proof is an adaptation of a contradiction and compactness argument that so far had been only used to prove estimates in Hölder spaces. This new approach is simpler than previous ones, and avoids the use of any interpolation theorem.
Bridging the Quality Gap: Robust Colon Wall Segmentation in Noisy Transabdominal Ultrasound
(Elsevier Ltd., 2025-10-01) Gago, Lucas; Fernández González, Miguel Á.; Engelmann, Justin; Remeseiro López, Beatriz; Igual Muñoz, Laura
Colon wall segmentation in transabdominal ultrasound is challenging due to variations in image quality, speckle noise, and ambiguous boundaries. Existing methods struggle with low-quality images due to their inability to adapt to varying noise levels, poor boundary definition, and reduced contrast in ultrasound imaging, resulting in inconsistent segmentation performance. We present a novel quality-aware segmentation framework that simultaneously predicts image quality and adapts the segmentation process accordingly. Our approach uses a U-Net architecture with a ConvNeXt encoder backbone, enhanced with a parallel quality prediction branch that serves as a regularization mechanism. Our model learns robust features by explicitly modeling image quality during training. We evaluate our method on the C-TRUS dataset and demonstrate superior performance compared to state-of-the-art approaches, particularly on challenging low-quality images. Our method achieves Dice scores of 0.7780, 0.7025, and 0.5970 for high, medium, and low-quality images, respectively. The proposed quality-aware segmentation framework represents a significant step toward clinically viable automated colon wall segmentation systems.
On the convergence of flow map parameterization methods for whiskered tori in quasi-periodic Hamiltonian systems
(Elsevier B.V., 2024-01-12) Fernández Viciana, Ana; Haro, Àlex; Mondelo Martell, Manel
We obtain an a-posteriori theorem for the existence of partially hyperbolic invariant tori in analytic Hamiltonian systems: autonomous, periodic, and quasi-periodic. The method of proof is based on the convergence of a KAM iterative scheme to solve the invariance equations of tori and their invariant bundles under the framework of the parameterization method. Starting from parameterizations analytic in a complex strip and satisfying their invariance equations approximately, we derive conditions for the existence of analytic parameterizations in a smaller strip satisfying the invariance equations exactly. The proof relies on the careful treatment of the analyticity loss with each iterative step and on the control of geometric properties of symplectic flavour. We also provide all the necessary explicit constants to perform computer-assisted proofs.
Explicit numerical computation of normal forms for Poincaré maps
(Elsevier B.V., 2025-05-10) Gimeno i Alquézar, Joan; Jorba i Monte, Àngel; Jorba Cuscó, Marc; Zou, Maorong
We present a methodology for computing normal forms in discrete systems, such as those described by Poincaré maps. Our approach begins by calculating high-order derivatives of the flow with respect to initial conditions and parameters, obtained via jet transport, and then applying appropriate projections to the Poincaré section to derive the power expansion of the map. In the second step, we perform coordinate transformations to simplify the local power expansion around a dynamical object, retaining only the resonant terms. The resulting normal form provides a local description of the dynamics around the object, and shows its dependence on parameters. Notably, this method does not assume any specific structure of the system besides sufficient regularity. To illustrate its effectiveness, we first examine the well-known Hénon–Heiles system. By fixing an energy level and using a spatial Poincaré section, the system is represented by a 2D Poincaré map. Focusing on an elliptic fixed point of this map, we compute a high-order normal form, which is a twist map obtained explicitly. This means that we have computed the invariant tori inside the energy level of the Poincaré section. Furthermore, we explore how both the fixed point and the normal form depend on the energy level of the Poincaré section, deriving the coefficients of the twist map as a power series of the energy level. This approach also enables us to obtain invariant tori inside nearby energy levels. We also discuss how to obtain the frequencies of the torus for the flow. We include a second example involving an elliptic periodic orbit of the spatial Restricted Three-Body Problem. In this case the map is 4D, and the normal form is a multidimensional twist map.
Periodic perturbation of a 3D conservative flow with a heteroclinic connection to saddle-foci
(Elsevier B.V., 2025-04-01) Murillo López, Ainoa; Vieiro Yanes, Arturo
The 2-jet normal form of the elliptic volume-preserving Hopf-zero bifurcation provides a one-parameter family of volume-preserving vector fields with a pair of saddle-foci points whose 2-dimensional invariant manifolds form a 2-sphere of spiralling heteroclinic orbits. We study the effect of an external periodic forcing on the splitting of these 2-dimensional invariant manifolds. The internal frequency (related to the foci and already presented in the unperturbed system) interacts with an external one (coming from the periodic forcing). If both frequencies are incommensurable, this interaction leads to quasi-periodicity in the splitting behaviour, which is exponentially small in (a suitable function of) the unfolding parameter of the Hopf-zero bifurcation. The corresponding behaviour is described by a Melnikov function. The changes of dominant harmonics correspond to primary quadratic tangencies between the invariant manifolds. Combining analytical and numerical results, we provide a detailed description of the asymptotic behaviour of the splitting under concrete arithmetic properties of the frequencies.
Safeguarding Autonomy: a Focus on Machine Learning Decision Systems
(Elsevier B.V., 2025-10-10) Subías Beltrán, Paula; Pujol Vila, Oriol; Lecuona Ramírez, Itziar de
As global discourse on AI regulation gains momentum, this paper focuses on delineating the impact of ML on autonomy and fostering awareness. Respect for autonomy is a basic principle in bioethics that establishes people as decision-makers. While the concept of autonomy in the context of ML appears in several European normative publications, it remains a theoretical concept that has yet to be widely accepted in ML practice. Our contribution is to bridge the gap between theory and practice in ML by encouraging the respect of autonomy in ML-aided decision-making. We do this by proposing a clear framework for operationalizing autonomy and identifying the conditioning factors that currently prevent it. Consequently, we focus on the different stages of the ML pipeline to identify the potential effects on ML end-users’ autonomy. To improve its practical utility, we propose a related question for each detected impact, offering guidance for identifying possible focus points to respect ML end-users autonomy in decision-making.
Formal stationary phase for the Mellin transform of a $\mathcal{D}$-module
(Research Institute for Mathematical Sciences, 2023-10-11) García López, Ricardo, 1962-
Given a holonomic $\mathbb{C}\left[z, z^{-1}\right]\left\langle\partial_z\right\rangle$-module $\mathbb{M}$, following Loeser and Sabbah (Comment. Math. Helv. 66 (1991), 458503), one can consider its Mellin transform, which is a difference system on the affine line over $\mathbb{C}$. In this note we prove a stationary phase formula, which shows that its formal behavior at infinity is determined by the local germs defined by $\mathbb{M}$ at its singular points.
Unit-Centric Regularization for Efficient Deep Neural Networks
(Institute of Electrical and Electronics Engineers (IEEE), 2025-07-21) Riera Molina, Carles Roger; Puertas i Prats, Eloi; Pujol Vila, Oriol
Deep neural networks excel by learning hierarchical representations, often requiring architectural enhancements like increased width, normalization layers, or skip connections, each adding complexity and computational cost. This paper proposes Jumpstart, a novel regularization technique that enables the use of simpler architectures by promoting efficient utilization of both network units and data points. The method penalizes units that become inactive (dead) or operate strictly in the linear regime, as well as data points whose activations within a layer are uniformly zero or strictly positive. This strategy enables the training of plain ReLU networks without relying on overparameterization, specialized initialization, normalization layers, or architectural modifications like skip connections. As a result, it promotes more efficient use of units and data, maintaining performance while avoiding waste of computational resources during both training and inference. On the ImageNet benchmark, it matches the top-1 accuracy of a standard ResNet50 with Batch Normalization and skip connections. On UCI tabular datasets, it consistently outperforms batch normalization and often surpasses residual connections. The method is evaluated using four global metrics: Dead Units, Linear Units, Trainability, and Convergence. Jumpstart significantly reduces the presence of inactive and linear units (0.07 and 0.12, respectively), outperforming most baselines and achieves superior trainability (1.0) and convergence (-0.03). These results demonstrate that simpler, regularized networks can maintain competitive accuracy while significantly lowering architectural complexity and computational burden. Jumpstart offers a sustainable and effective alternative to conventional deep learning design strategies, facilitating efficient training without compromising performance.
Hodge–Lyubeznik numbers
(Elsevier Masson, 2025-03-25) García López, Ricardo, 1962-; Sabbah, Claude
We define a Hodge-theoretical refinement of the Lyubeznik numbers for local rings of complex algebraic varieties. We prove that these numbers are independent of the choices made in their definition and that, for the local ring of an isolated singularity, they can be expressed in terms of the Hodge numbers of the cohomology of the link of the singularity. We give examples of isolated singularities with the same Lyubeznik numbers but different Hodge–Lyubeznik numbers.
Bridging gaps in youth mental health care: YOUTHreach—a comprehensive European strategy
(Springer Verlag, 2026-04-25) Oidermaa, Anna-Kaisa; Bechdolf, Andreas; Evers, Silvia; van Mastrigt, Ghislaine; Horstkötter, Dorothee; Janssen, Ricky; Bulgheroni, Maria; McDaid, David; Boehnke, Jan R.; McGorry, Patrick; van Amelsvoort, Therese; Boonstra, Anouk; Lekadir, Karim, 1977-; Ruiz Pujadas, Esmeralda; Broome, Matthew R.; Griffiths, Sian Lowri; Donohoe, Gary; Popma, Arne; Girolamo, Giovanni de; Díaz Caneja, Covadonga M.; Álvarez Jiménez, Mario; AEGEE; Schick, Anita; Reininghaus, Ulrich; Leijdesdorff, Sophie
Europe is facing a mental health crisis that will last for decades, impacting the long-term health outcomes, wellbeing and economic productivity of our current generation of young people. Yet, large-scale, comparative research of youth-friendly mental health interventions is lacking. The YOUTHreach consortium aims to bridge this gap and provide a comprehensive European strategy. For this purpose, YOUTHreach will evaluate the clinical effectiveness and cost-effectiveness of three existing and accessible innovative interventions for prevention and early intervention of mental ill-health in youth, developed and tested in co-creation with youth: 1) YEAH, walk-in youth mental health support centres; 2) SELFIE, a transdiagnostic blended ecological momentary intervention; and 3) MOST, a clinical and peer-moderated digital youth mental health platform. In addition, feasibility and acceptability at new sites across Europe will be tested. Furthermore, in partnership with young people, best practice recommendations will be developed based on existing and new data and built into an integrated European youth mental health framework. Finally, awareness and accessibility of these interventions among policymakers, healthcare professionals, the general public, and youth—the target group—will be raised. YOUTHreach aims to contribute towards transformation of the present traditional mental healthcare system and providing the next generation with a better perspective in terms of health, wellbeing and productivity.
The canonical module of GT-varieties and the normal bundle of RL-varieties.
(Springer Verlag, 2021) Colarte Gómez, Liena; Miró-Roig, Rosa M. (Rosa Maria)
In this paper, we study the geometry of GT-varieties with group a finite cyclic group of order d. We prove that the homogeneous ideal of is generated by binomials of degree at most 3 and we provide examples reaching this bound. We give a combinatorial description of the canonical module of the homogeneous coordinate ring of and we show that it is generated by monomial invariants of of degree d and 2d. This allows us to characterize the Castelnuovo–Mumford regularity of the homogeneous coordinate ring of . Finally, we compute the cohomology table of the normal bundle of the so-called RL-varieties. They are projections of the Veronese variety which naturally arise from level GT-varieties.
Lacunary polynomials in L1: Geometry of the unit sphere
(Elsevier B.V., 2021-04-16) Dyakonov, Konstantin M.
Let Λ be a finite set of nonnegative integers, and let be the linear hull of the monomials with , viewed as a subspace of on the unit circle. We characterize the extreme and exposed points of the unit ball in .
A counterexample to Payne's nodal line conjecture with few holes
(Elsevier B.V., 2021) Dahne, Joel; Gómez Serrano, Javier; Hou, Kimberly
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
Gaussian lower bound and positivity of the density of stochastic delay differential equations driven by a fractional Brownian motion
(Sveuilište Josipa Jurja Strossmayera u Osijeku, 2026-04-02) Burés Mogollón, Òscar; Rovira Escofet, Carles
In this paper, we prove that the density of a stochastic delay differential equation driven by a fBm with Hurst parameter > 1/2 is strictly positive combining Nourdin-Viens’ and Kohatsu-Higa’s method.

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